@Magnus. Not a stupid question - but I don't have any statistics. The 1800s wer just a mess when it comes to names. Big social transition, big transition in naming practices. The story about the girl does not surprise me.
My grandfather, Gustaf Persson, was born in 1892, to Per Gustav Larsson. His sister, born in 1890 was Gustavsson before she married. So the powers that be looked at different parts of their father's name - for my granddads part he was surnamed when he did his military service in 1913. You know, children in the olden days did NOT have a last name at birth at all - they got it when they started to earn their own living.